Pollution exists in every large city. The smog ("nefos") has been loomed over Athens since a lot of years... The building boom in '50s and in '60s had brought an anarchy construction and there are not anymore many parks and green belts.
The governments try to solve the problem, but it is not so easy... It becomes horrible during a hot summer day, especially when there is no any wind...
Greeks are heavy smokers. And very "democratic" about it, too... they don't mind you eating like they're smoking! You will find that, unlikely to most countries and in most indoor restaurants, cafes, etc. the non smoking section is the one right next to the WC. There is no use arguing about it. Be prepared to enter the nicotine world where smokers' constitutional rights beat the living hell out of those of the non-smokers.
In an effort to reduce the health hazard, government banned smoking from civil/public services (although you will always see the "rebels" who moved their desk next to the open window and smoke two packets in their 8-hour shift). Smoking is also banned in taxis. You can and should demand from your taxi driver to throw away his cigarette as soon as you enter his cab. Not before because you might loose him! If the weather is nice and he asks you to keep his cancer-tube outside his window, it's in your good will whether he can keep it or not.
Athens has air that is not quite up to breathing standards. Anyone with asthma or other respiratory problems should take care. The worst time for smog is in July and August when it is extremely hot.
If you are staying in Athens for an extended period of time, it might be a good idea to leave the city every few days or so to give your lungs a break. I recommend Sounio or a seaside town, a nearby island like Aegina, Poros, or Hydra, or up in the mountains near Athens.
In this picture I took from my flight taking off in Athens, you can see how thick the air can be.